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(a) find parametric equations for the line that passes through the point (−2, 5) and is parallel to the vector <3, −8>. (enter your answer as a comma-separated list of equations where x and y are in terms of the parameter t.)

Respuesta :

sqdancefan
= <-2 +3t, 5 -8t>

Multiply the direction vector by the parameter and add it to the given point.

The parametric equations for the line are:

[tex]x(t) = -2 + 3t[/tex]

[tex]y(t) = 5 - 8t[/tex]

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A line that passes through a point [tex](x_0, y_0)[/tex] and is parallel to a vector (a,b) has parametric equations given by:

[tex]x(t) = x_0 + at[/tex]

[tex]y(t) = y_0 + bt[/tex]

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  • Passes through the point (-2,5), thus [tex]x_0 = -2, y_0 = 5[/tex]
  • Parallel to vector <3, -8>, thus [tex]a = 3, b = -8[/tex]

The parametric equations are:

[tex]x(t) = -2 + 3t[/tex]

[tex]y(t) = 5 - 8t[/tex]

A similar problem is given at https://brainly.com/question/15986055

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